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The macroscopical properties of complex system lie on the interaction structurebetween individuals, which can be described勿complex networks. So the in-vestigation of complex network has been the basis of studying complexity. Infact, complex networks can describe a wide range of systems in nature and soci-ety, such as biology system, society system and so on. One-mode network, theusual way to describe complex networks, only considers one kind vertices in thenetworks. However, some of realistic systems naturally show bipartite structure,which have two different sets of nodes and links only exit between nodes belongto different sets. As an important class of complex networks, bipartite networksavoids the drawbacks brought勿projecting into one-mode networks and providesa new way to depict properties and function of systems.
In this thesis, after introducing some formed notions and properties of bi-partite networks in Chapter 2, we begin Chapter 3 with the study of clusteringcoefficient and community structure on bipartite networks. In this part, based onthe approach of standard clustering coefficient of one-mode networks, a definitionof the clustering coefficient for bipartite networks based on the fraction of squaresis proposed. In order to detect community structures in bipartite networks, twodifferent edge clustering coefficients LC9 and LC3 of bipartite networks are de-fined, which axe based on squares and triples respectively. With the algorithmof cutting the edge with the least clustering coefficient, communities in artificialand real world networks are identified.
In Chapter 4,we mainly discuss evolution models of bipartite networks.First, we introduce and analyze 6 Real-World Bipartite Networks. According tothe relationship of two sets of nodes, they are classified to two types. dependencebipartite networks and independence bipartite networks. Then by analyzing. theresults show that the actors nodes have scale-free property in the dependencenetworks. In order to understand this behavior, two growing bipartite modelswithout the preferential attachment principle are proposed. The models showthe scale-free phenomena in actorss degree distribution. It also gives well qual-itatively consistent behavior with the empirical results.
At last, we discuss the bootstrap percolation on bipartite networks in Chap-ter 5. The rule of bootstrap percolation model on bipartite networks is introducedfirstly. Then we obtain the analytical results and simulation results of whole pro-cess, the size of final active fraction Sa shows a jump as a function of initial activeprobability f . Apart considering the influences to above behaviors brought勿the different values of the network size, the active threshold S2 and the meandegree，we got there was a special point where the jump disappears as theactive threshold growing or the mean degree decreasing.Keywords: Complex networks, Bipartite networks, Empirical networks, Clus-tering coefficient, Community structure, Evolving model, Bootstrap percolation,Phase transition